(672d) Using a PBM to Describe the Drying Behaviour of Wet Pharmaceutical Granules: Scenario Analysis and GSA

During the production of pharmaceutical tablets, a drying step is necessary when using wet granulation. Fluidized bed drying is a commonly used technique for this purpose. However, the drying technique and drying process settings may have a significant influence on the resulting properties of the granules and tablets [1]. In view of the trend towards continuous production, process knowledge is required and, as such, the necessity to develop mechanistic models is emerging. These models can assist in gaining process knowledge and, at a later stage be helpful for introducing process control based on on-line measurements and real-time adaptations of sensitive process variables. Indeed, mechanistic models include the impact of input variables on the process variables of interest, i.e. the output variables.

The case under study is a fluidized bed drying system as part of a full continuous from-powder-to-tablet manufacturing line (ConsiGma^TM, Collette^TM, GEA Pharma Systems, Wommelgem, Belgium). The system consists of three parts: a continuous twin screw granulator (high shear), a six-segmented fluidized bed dryer system and a discharge system. The drying system consists of six segments, which are fed consecutively with continuously produced wet granules, hence allowing continuous drying.

A model describing the drying behaviour of single pharmaceutical granules was developed earlier [2]. This model consists of two sub-models, one for the fast drying phase and one for the second and slow drying phase. The model was calibrated and validated using experimental data, after which a model reduction was performed resulting in an empirical reduced model [3]. This step was necessary in order to incorporate it in a Population Balance Model (PBM). The PBM predicts the evolution of the moisture content distribution as function of gas temperature and velocity. Degrees of freedom of the PBM are the particle radius, initial moisture content and filling time.

In this work we investigate the influence of the gas temperature and gas velocity on the distribution of the moisture content after drying. This  distribution is of particular interest as it directly influences the quality of the final tablet product.

The Population Balance Equations (PBEs) are solved using the Method of Characteristics (MOC), which uses a moving grid. A grid size of 150 was used.

First, a scenario analysis was defined by using user-defined gas temperature and gas velocity input time series. These intended to mimick the dynamic local gas temperature and velocity the particle is exposed to when travelling along its path through the fluidized bed. Currently, these dynamic patterns are based on expert judgment, but in a later stage these should be derived from a Computational Fluid Dynamics (CFD) model. The objective here is to investigate the impact of fluctuating conditions on the characteristics of the distribution. It should be regarded as a proof of principle of using the calibrated and validated drying model under dynamic conditions of gas temperature and velocity.

A higher gas temperature increases the evaporation rate and as such the moisture content decreases faster. A constant gas temperature also benefits the drying rate. However, in both cases the standard deviation of the resulting distribution is larger compared to a standard case, meaning that some particles are considerably more dry compared to others which is undesired. An increase of 10°C for the gas temperature increases the standard deviation significantly over the entire time range. The increase of the standard deviation occurs during the filling period; when a high gas temperature is used, the moisture content will drop faster and the distribution will broaden more. A lower gas temperature slows down the fast drop in moisture content, and as such, the distribution will be narrower.

Focusing on the effect of the gas velocity, almost no difference can be detected in the mean and the standard deviation of the distribution of the moisture content when the gas velocity is varied. The gas velocity only has an influence on the first drying period, as the gas velocity is not involved in the equation for the second drying phase.

Second, a (global) sensitivity analysis (GSA) was performed. This entails the study of how the uncertainty in the output of a model (numerical or otherwise) can be apportioned to different sources of uncertainty in the model input, model structure or parameters [4]. A GSA provides useful information if one is to reduce the model output uncertainty as it points towards the source of the output uncertainty. Several tools to perform a GSA exist. Graphical GSA tools, such as Contribution to Sample Mean (CSM) and Contribution to Sample Variance (CSV) plots, are interesting since they only require a relatively low number of simulations.

Two-dimensional dotty plots are interesting to understand the influence of the input factors on the output. These plots showed that a small particle radius is important to allow a short drying time, and as such a low value for the mean of the distribution of the moisture content. Larger particle radii can be compensated for by a higher gas temperature at which the drying is performed. However, a low gas temperature governs a narrow distribution of the moisture content which clearly results in a trade-off between particle size and gas temperature. A trend can be detected for the combination of gas temperature and the filling time. When the filling time is large, a narrow distribution can be obtained by imposing a low gas temperature. In general a low value of the filling time is interesting to obtain a narrow distribution.

Based on the CSM the particle radius is the most influential parameter, followed by the gas temperature. The variance of the distribution is most sensitive towards the gas temperature, but also the filling time is influential on the variance.

Based on the GSA results, it could be concluded that the gas temperature is obviously the most sensitive parameter. The gas temperature is as such an important factor for process control and changing the process during operation. The gas temperature can easily be varied during operation based on real-time measurements. Particle radius is also important which can be fed back to the optimization of the granulation step. This clearly illustrates the necessity of an integrated approach when optimizing the coupled process.

[1] S.T.F.C. Mortier et al., Mechanistic modelling of fluidized bed drying processes of wet porous granules: A review, Eur. J. Pharm. Biopharm. 79 (2011) 205-225.

[2] S.T.F.C. Mortier et al., Mechanistic modelling of the drying behaviour of single pharmaceutical granules, Eur. J. Pharm. Biopharm. 80 (3) (2012) 682-689.

[3] S.T.F.C. Mortier et al., Reduction of a single granule drying model: An essential step in preparation of a PBM with a continuous growth term, AIChE J. 59 (4) (2013) 1127-1138.

[4] A. Saltelli et al., Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models (2004).